Standard Deviation Calculator
Paste or type your numbers to get the standard deviation (sample and population), mean, median, mode, quartiles, variance, and more, with the steps shown.
Separate numbers with commas, spaces, or new lines. You can paste a column straight from Excel or Google Sheets.
Sample if it's part of a bigger group (most class and survey data). Population if it's every member of the group.
Show the steps
How it works
Sample or population standard deviation?
Use the sample standard deviation (s) when your numbers are a sample from a larger group. It divides by n − 1, which corrects for the sample usually being less spread out than the whole group. Use the population standard deviation (σ) only when you have data for every member of the group. It divides by n.
What does standard deviation tell me?
It measures how spread out the numbers are around the mean. A small standard deviation means the values sit close to the average; a large one means they're widely scattered. For bell-shaped data, about 68% of values fall within one standard deviation of the mean, and about 95% within two.
How are the quartiles calculated?
Q1 is the median of the lower half of the sorted data and Q3 the median of the upper half, leaving out the overall median when there's an odd count. Many school calculators use this method. Other software (like Excel's QUARTILE.INC) uses slightly different rules, so quartiles can differ a little between tools.
How are outliers found?
Using the 1.5 × IQR rule: a value is flagged if it's more than 1.5 times the interquartile range below Q1 or above Q3.